...a modified probabilistic construction which can be derandomized to yield a polynomial-time algorithm for the determination of such a basis up to any desired inte
4 KB (658 words) - 19:37, 29 March 2024
The polynomial $ H _ {n} ( x) $
5 KB (663 words) - 07:13, 20 April 2024
The Legendre polynomial of order $ n $
5 KB (670 words) - 17:45, 13 January 2024
is a symmetric polynomial of degree 4 in $ x $
is a polynomial in $ X $.)
13 KB (1,798 words) - 19:06, 26 January 2022
may increase at infinity as a polynomial (in this case a dispersion relation with subtractions is obtained), the bou
4 KB (620 words) - 11:56, 26 March 2023
...heory [[#References|[a24]]], [[#References|[a29]]], [[#References|[a31]]], polynomial hyponormality [[#References|[a11]]], and joint hyponormality [[#References|
...s|[a22]]]; in particular, D. Hilbert (1888) established the existence of a polynomial, non-negative on the real plane, that cannot be represented as a sum of squ
23 KB (3,450 words) - 17:45, 1 July 2020
is the minimal symmetric polynomial containing the monomials $ t _ {1} ^ {i _ {1} } \dots t _ {k} ^ {i _ {k}
5 KB (680 words) - 08:07, 6 June 2020
...ven by an equation $f ( X , Y ) = 0$ where $f$ is an irreducible bivariate polynomial of degree $n$ over a ground field $k$ (cf. also [[Algebraic curve|Algebraic
...n be parametrized rationally. To this end one first notes that a bivariate polynomial of degree $m$ has
16 KB (2,510 words) - 17:43, 1 July 2020
...itive integer. The ring of differential operators with coefficients in the polynomial ring $ K [ x ] = K [ x _ {1} \dots x _ {n} ] $
such that a polynomial coefficient $ p _ \alpha ( x) $
28 KB (4,182 words) - 19:30, 19 January 2024
...one $C(X,x)$ to $X$ at $x$ is given by the ideal of initial forms of the [[polynomial]]s in $\mathfrak{A}$. (If $F = F_k + F_{k+1} + \cdots$ is the expansion of
4 KB (653 words) - 13:02, 17 June 2016
such that every homogeneous polynomial $ f ( X _ {1} \dots X _ {n} ) $
field if every homogeneous polynomial $ f( X _ {1} \dots X _ {n} ) $
10 KB (1,605 words) - 16:57, 13 January 2024
the adjunction to the field $\R$ of a root $i$ of the polynomial
polynomial with coefficients in $\C$ splits into linear factors. The
14 KB (2,281 words) - 09:55, 26 March 2023
a polynomial in $ y $
is holomorphically equivalent to a polynomial normal representation. In this setting the Poincaré condition (i.e., belon
11 KB (1,659 words) - 05:14, 24 February 2022
...ture is considered as an analogue of Weil's result that the characteristic polynomial of the Frobenius automorphism acting on the Jacobian of a curve over a fini
...n $\mathcal{O}$. $P ( T ) \in \mathcal{O} [ T ]$ is called a distinguished polynomial if $P ( T ) = T ^ { n } + a _ { n - 1 } T ^ { n - 1 } + \ldots + a _ { 0 }
19 KB (2,876 words) - 05:38, 15 February 2024
be a polynomial in $ n $
does not exceed the degree of the polynomial $ f(x) $.
19 KB (3,006 words) - 06:05, 26 May 2024
...is equal to its genus and coincides with half the degree of the Alexander polynomial (cf. [[Alexander invariants|Alexander invariants]]). A slice knot (cf. [[Co
is the Alexander polynomial (cf. [[Alexander invariants|Alexander invariants]]). The $ V $-
11 KB (1,680 words) - 10:46, 20 January 2024
is any real number, the solution of (12) is a polynomial $ T _ {n} ( x) $
a Chebyshev polynomial of the first kind), defined by
14 KB (1,916 words) - 19:59, 12 January 2024
vertices), and the totality of these characteristics can be specified by the polynomial $ \sum _ {k} f _ {k} ( G) x ^ {k} $—
5 KB (780 words) - 20:06, 15 March 2023
is called an interpolation polynomial in the system $ \{ \phi _ {i} ( x) \} $
that is a polynomial of degree three on each segment $ [ x _ {k-} 1 , x _ {k} ] $,
26 KB (3,882 words) - 22:13, 5 June 2020
...by annihilating sequences of ideals [[#References|[a1]]]. The radical of a polynomial ring $ R [ x] $
5 KB (764 words) - 08:09, 6 June 2020